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Interpolation among reduced-order matrices to obtain parameterized models for design, optimization and probabilistic analysis. (English) Zbl 1188.65110

Summary: Model reduction has significant potential in design, optimization and probabilistic analysis applications, but including the parameter dependence in the reduced-order model (ROM) remains challenging. In this work, interpolation among reduced-order matrices is proposed as a means to obtain parameterized ROMs. These ROMs are fast to evaluate and solve, and can be constructed without reference to the original full-order model. Spline interpolation of the reduced-order system matrices in the original space and in the space tangent to the Riemannian manifold is compared with Kriging interpolation of the predicted outputs. A heuristic criterion to select the most appropriate interpolation space is proposed. The interpolation approach is applied to a steady-state thermal design problem and probabilistic analysis via Monte Carlo simulation of an unsteady contaminant transport problem.

MSC:

65L80 Numerical methods for differential-algebraic equations
35K20 Initial-boundary value problems for second-order parabolic equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65D05 Numerical interpolation
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65C05 Monte Carlo methods

Software:

MATLAB expm; DACE
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References:

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